# Class 10

Explore popular questions from Introduction to Trigonometry for Class 10. This collection covers Introduction to Trigonometry previous year Class 10 questions hand picked by experienced teachers.

## Mathematics

Introduction to Trigonometry

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Q 1. If {tex} \sin \theta + \cos \theta = \sqrt { 2 } \cos \left( 90 ^ { \circ } - \theta \right) {/tex} then {tex} \cot \theta {/tex} is equal to

A

{tex} \frac { 1 } { \sqrt { 2 } } {/tex}

B

{tex} \frac { \sqrt { 3 } } { 2 } {/tex}

C

{tex} \frac { 1 } { \sqrt { 2 } - 1 } {/tex}

{tex} \sqrt { 2 } - 1 {/tex}

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Q 2. If {tex} \sec \theta + \tan \theta = x {/tex} then the value of {tex} \sec \theta - \tan \theta {/tex} is equal to

A

{tex} - x {/tex}

{tex} \frac { 1 } { x } {/tex}

C

{tex} - \frac { 1 } { x } {/tex}

D

{tex} \sqrt { x } {/tex}

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Q 3. If {tex} \mathrm { x } = \mathrm { a } \sin \theta {/tex} and {tex} \mathrm { y } = \mathrm { b } \cos \theta , {/tex} then the value of {tex} \mathrm { b } ^ { 2 } \mathrm { x } ^ { 2 } + \mathrm { a } ^ { 2 } \mathrm { y } ^ { 2 } {/tex} is

{tex} \mathrm{a ^ { 2 } b ^ { 2 }} {/tex}

B

{tex}\mathrm{ a b} {/tex}

C

{tex} \mathrm{\frac { 1 } { a ^ { 2 } b ^ { 2 } }} {/tex}

D

{tex} \mathrm {\frac { 1 } { \mathrm { ab } }} {/tex}

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Q 4. An equation is called an identity if

If is true for all values of variable

B

Not for all values of variabls but some value of variable

C

Exactly one value of variables

D

Exactly two value of variables

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Q 5. If {tex} x = ( \sec A + \tan A ) ( \sec B + \tan B ) ( \sec C + \tan C ) ;  y = ( \sec A - \tan A ) ( \sec B - \tan B ) ( \sec C - \tan C ) {/tex} and {tex} x = y {/tex} then {tex} x {/tex} and {tex} y {/tex} is equal to

{tex} \pm 1 {/tex}

B

{tex}0{/tex}

C

{tex} \pm 2 {/tex}

D

None of these

##### Explanation

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Q 6. If {tex} x = \cot ^ { 2 } \theta - \frac { 1 } { \sin ^ { 2 } \theta } {/tex} than the value of {tex} x {/tex} is

A

{tex} 1 {/tex}

{tex} - 1 {/tex}

C

{tex} \pm 1 {/tex}

D

zero

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Q 7. {tex} 2 \left( \sin ^ { 6 } \theta + \cos ^ { 6 } \theta \right) - 3 \left( \sin ^ { 4 } \theta + \cos ^ { 4 } \theta \right) {/tex} is equal

A

zero

B

1

-1

D

None of these

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Q 8. {tex} \sqrt { \frac { 1 + \sin \theta } { 1 - \sin \theta } } {/tex} is equal to

{tex} \sec \theta + \tan \theta {/tex}

B

{tex} \sec \theta - \tan \theta {/tex}

C

{tex} \sec ^ { 2 } \theta + \tan ^ { 2 } \theta {/tex}

D

{tex} \sec ^ { 2 } \theta - \tan ^ { 2 } \theta {/tex}

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Q 9. {tex} \sec ^ { 4 } A - \sec ^ { 2 } A {/tex} is equal to

A

{tex} \tan ^ { 2 } A - \tan ^ { 4 } A {/tex}

B

{tex} \tan ^ { 4 } A - \tan ^ { 2 } A {/tex}

{tex} \tan ^ { 4 } A + \tan ^ { 2 } A {/tex}

D

{tex}- \tan ^ { 2 } A - \tan ^ { 4 } A {/tex}

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Q 10. {tex} \cos ^ { 4 } A - \sin ^ { 4 } A {/tex} is equal to

A

{tex} 2 \cos ^ { 2 } A + 1 {/tex}

{tex} 2 \cos ^ { 2 } A - 1 {/tex}

C

{tex} 2 \sin ^ { 2 } - 1 {/tex}

D

{tex} 2 \sin ^ { 2 } A + 1 {/tex}

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Q 11. {tex} \mathrm { P } = ( 1 + \cot \theta - \cosec \theta ) ( 1 + \tan \theta + \sec \theta ) {/tex}
the value of {tex}\mathrm P {/tex} is equal to

A

1

2

C

4

D

zero

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Q 12. {tex} ( \cosec \theta - \sin \theta ) ( \sec \theta - \cos \theta ) ( \tan \theta + \cot \theta ) {/tex} is equal to

A

zero

1

C

-1

D

none of these

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Q 13. The value of is equal to:

A

{tex} \sqrt { 3 } {/tex}

{tex} - \sqrt { 3 } {/tex}

C

{tex} \frac { 1 } { \sqrt { 3 } } {/tex}

D

{tex} - \frac { 1 } { \sqrt { 3 } } {/tex}

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Q 14. The expression {tex} \sqrt { \sin ^ { 2 } ( 37.5 ) ^ { \circ } + \cos ^ { 2 } ( 37.5 ) ^ { \circ } } + \sqrt { \cos ^ { 2 } ( 37.5 ) ^ { \circ } + sin ^ { 2 } ( 37.5 ) ^ { \circ } } {/tex} simplifies to:

A

an irrational number

B

a prime number

a natural number which is not composite

D

a real number of the form {tex} a + \sqrt { b } {/tex}

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Q 15. If {tex} 15 \cos ^ { 4 } \alpha + 10 \sin ^ { 4 } \alpha = 6 , {/tex} then the value of {tex}8 \sec ^ { 6 } \alpha + 27 \cosec ^ { 6 } \alpha {/tex} is

A

200

250

C

220

D

None of these

##### Explanation

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Q 16. If {tex} a = \frac { \cot \theta } { \cot \theta - \cot 3 \theta }\ \ \& \ b = \frac { \tan \theta } { \tan \theta - \tan 3 \theta } {/tex} then {tex} \sqrt { a + b } {/tex} is equal to

A

{tex} \pm 2 {/tex}

B

{tex} - 2 {/tex}

{tex} + 1 {/tex}

D

{tex} - 1 {/tex}

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Q 17. If {tex} a \cos \theta - b \sin \theta = C {/tex} then {tex} a \sin \theta + b \cos \theta = {/tex}

A

{tex} \pm \sqrt { a ^ { 2 } + b ^ { 2 } + c ^ { 2 } } {/tex}

{tex} \pm \sqrt { a ^ { 2 } + b ^ { 2 } - c ^ { 2 } } {/tex}

C

{tex} \pm \sqrt { c ^ { 2 } - a ^ { 2 } - b ^ { 2 } } {/tex}

D

None of these

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Q 18. If {tex} a \cos \theta + b \sin \theta = 4 {/tex} and {tex} a \sin \theta - b \cos \theta = 3 {/tex} then {tex} \left( a ^ { 2 } + b ^ { 2 } \right) {/tex} is equal to

A

7

B

12

25

D

None of these

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Q 19. If {tex} \cos A = \frac { 4 } { 5 } {/tex} then the value of {tex} \tan A {/tex} is :

A

{tex} \frac { 3 } { 5 } {/tex}

{tex} \frac { 3 } { 4 } {/tex}

C

{tex} \frac { 4 } { 3 } {/tex}

D

{tex} \frac { 1 } { 8 } {/tex}

##### Explanation

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Q 20. The value of the expression [cosec {tex} \left( 75 ^ { \circ } + \theta \right) {/tex} {tex} \left. - \sec \left( 15 ^ { \circ } - \theta \right) - \tan \left( 55 ^ { \circ } + \theta \right) + \cot \left( 35 ^ { \circ } - \theta \right) \right] {/tex} is :

A

{tex} - 1 {/tex}

{tex} 0 {/tex}

C

{tex} 1 {/tex}

D

{tex} \frac { 3 } { 2 } {/tex}

##### Explanation

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Q 21. Given that {tex} \sin \theta = \frac { a } { b } {/tex} then {tex} \cos \theta {/tex} is equal to

A

{tex} \frac { b } { \sqrt { b ^ { 2 } - a ^ { 2 } } } {/tex}

B

{tex} \frac { b } { a } {/tex}

{tex} \frac { \sqrt { b ^ { 2 } - a ^ { 2 } } } { b } {/tex}

D

{tex} \frac { a } { \sqrt { b ^ { 2 } - a ^ { 2 } } } {/tex}

##### Explanation

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Q 22. The value of (tan {tex} \left. 1 ^ { \circ } \tan 2 ^ { \circ } \tan 3 ^ { \circ } \dots \tan 89 ^ { \circ } \right) {/tex} is :

A

{tex} { 0 } {/tex}

{tex}1{/tex}

C

{tex}2{/tex}

D

{tex} \frac { 1 } { 2 } {/tex}

##### Explanation

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Q 23. If {tex} \Delta A B C {/tex} is right angled at {tex} C , {/tex} then the value of {tex} \cos {/tex} {tex} ( A + B ) {/tex} is :

{tex} 0{/tex}

B

{tex} 1{/tex}

C

{tex} \frac { 1 } { 2 } {/tex}

D

{tex} \frac { \sqrt { 3 } } { 2 } {/tex}

##### Explanation

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Q 24. If {tex} \sin A + \sin ^ { 2 } A = 1 , {/tex} then the value of the expression {tex} \left( \cos ^ { 2 } A + \cos ^ { 4 } A \right) {/tex} is :

{tex} 1{/tex}

B

{tex} \frac { 1 } { 2 } {/tex}

C

{tex} 2{/tex}

D

{tex} 3{/tex}

##### Explanation

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Q 25. Given that {tex} \sin \alpha = \frac { 1 } { 2 } {/tex} and {tex} \cos \beta = \frac { 1 } { 2 } {/tex}, then the value of {tex} ( \alpha + \beta ) {/tex} is :

A

{tex} 0 ^ { \circ } {/tex}

B

{tex} 30 ^ { \circ } {/tex}

C

{tex} 60 ^ { \circ } {/tex}

{tex} 90 ^ { \circ } {/tex}